Chapter 0.4, Problem 38E

To determine

To decide: if the given statement is True or False.

Answer to Problem 38E

True

Explanation of Solution

Given information:

The given statement is:

“The parametric curve $x=2\cos \left(-t\right),y=2\sin \left(-t\right),0\le t\le 2\pi$ is traced clockwise.”

To check if the given parametric curve is traced clockwise, list a few coordinates for $\left(x,y\right)$ in the given interval and observe the direction it will move.

t	$\left(x,y\right)$
0	$\left(2,0\right)$
$\frac{\pi }{4}$	$\left(\sqrt{2},-\sqrt{2}\right)$
$\frac{\pi }{2}$	$\left(0,-2\right)$

Observing these coordinates, it can be easily determined that the curve is traced clockwise.

Hence, the given statement is true.